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Diketahui kubus ABCD.EFGH dengan panjang rusuk . Titik M adalah titik potong garis AC dan BD, sedangkan titik N adalah titik potong garis EG dan HF. Jarak garis EM dan garis CN adalah ...

Pertanyaan

Diketahui kubus ABCD.EFGH dengan panjang rusuk 7 space cm. Titik M adalah titik potong garis AC dan BD, sedangkan titik N adalah titik potong garis EG dan HF. Jarak garis EM dan garis CN adalah ...

  1. 7 over 2 space cm

  2. 7 space cm

  3. 7 over 2 square root of 2 space cm

  4. 7 square root of 2 space cm

  5. 7 over 3 square root of 3 space cm

Pembahasan Soal:

Perhatikan pada gambar, 

Titik M merupakan titik potong garis AC dan BD.

Titik M terletak di tengah garis AC, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell A M end cell equals cell C M equals 1 half A C end cell row blank blank blank row cell A C end cell equals cell square root of A B squared plus B C squared end root end cell row cell A C end cell equals cell square root of 7 squared plus 7 squared end root end cell row cell A C end cell equals cell square root of 2 cross times 7 squared end root end cell row cell A C end cell equals cell 7 square root of 2 end cell row blank blank blank row cell A M end cell equals cell C M equals 1 half A C end cell row blank equals cell 1 half cross times 7 square root of 2 end cell row blank equals cell 7 over 2 square root of 2 end cell end table 

Sehingga, dengan menggunkana Pythagoras:

table attributes columnalign right center left columnspacing 0px end attributes row EM equals cell square root of AE squared plus AM squared end root end cell row blank equals cell square root of 7 squared plus open parentheses fraction numerator 7 square root of 2 over denominator 2 end fraction close parentheses squared end root end cell row blank equals cell square root of 7 squared plus fraction numerator 7 squared cross times 2 over denominator 4 end fraction end root end cell row blank equals cell square root of 7 squared cross times 1 plus 7 squared cross times 1 half end root end cell row blank equals cell square root of 7 squared open parentheses 1 plus 1 half close parentheses end root end cell row blank equals cell square root of 7 squared open parentheses 3 over 2 close parentheses end root end cell row blank equals cell 7 fraction numerator square root of 3 over denominator square root of 2 end fraction end cell row blank equals cell 7 fraction numerator square root of 3 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell 7 over 2 square root of 6 end cell end table  

Perhatikan ilustrasi di bawah ini:

 Dengan menggunakan rumus luas segitiga:

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 half M N times N E end cell equals cell 1 half cross times E M times t end cell row cell 7 over 2 square root of 2 times 7 end cell equals cell 7 over 2 square root of 6 times t end cell row cell 7 square root of 2 end cell equals cell square root of 6 t end cell row t equals cell fraction numerator 7 square root of 2 over denominator square root of 6 end fraction end cell row blank equals cell fraction numerator 7 over denominator square root of 3 end fraction end cell row blank equals cell 7 over 3 square root of 3 space cm end cell end table

Sehingga, jarak Em dan CN adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 7 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cm end table

Jadi, jawaban yang tepat adalah E

 

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 20 Juli 2021

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